Exact stiffness-matrix of two nodes Timoshenko beam on elastic medium. An analogy with Eringen model of nonlocal Euler-Bernoulli nanobeams

摘要

The paper deals with a general method to obtain a closed-form analytical solution of the problem of bending of a shear deformable beam resting on an elastic medium. Within a well posed analytical framework, the basic equations governing the interaction problem, can be obtained in strong form by a differential formulation based on both the constitutive equation of the Timoshenko beam and the direct and inverse constitutive equation of the supporting local elastic medium.